Free Printable Midterm Exam Reviewer

1.

Consider the given graph below. Determine if the relation defines y as a function of x.

a)

Yes

b)

No

c)

Neither

d)

Both 1 and 2

2.

If a function is defined as f(x) = 3x - 5, what is the range of f when x is restricted to the domain of [1, 3]?

a)

[-2, 4]

b)

[0, 4]

c)

[0, 6]

d)

[-2, 6]

3.

For the function h(x) = 1/(x - 3), what value of x makes the function undefined?

a)

3

b)

0

c)

-3

d)

1

4.

What is the Domain of this linear function?

a)

$-6\le x\le6$

b)

$0\le y\le6$

c)

$0\le y\le6$

d)

$-6\le y\le6$

5.

What is the Range of this linear function?

a)

-6 ≤ y ≤ 6

b)

0 ≤ y ≤ 6

c)

0 ≤ x ≤ 6

d)

-6 ≤ x ≤ 6

6.

Given $g\left(x\right)=\sqrt[]{x-5}$ , the domain is restricted so that x ≥ (a) .

7.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

8.

Simplify
(3x³y⁵)⁴

a)

3x¹²y²⁰

b)

81x¹²y²⁰

c)

12x¹²y²⁰

d)

81x⁷y⁹

9.

Write 0.0003 in scientific notation.

a)

3 x 10⁴

b)

3 x 10^-4

c)

0.3 x 10³

d)

0.3 x 10^-3

10.

Write 7,000,000 in scientific notation.

a)

0.7 x 10⁷

b)

7 x 10^-6

c)

7 x 10⁶

d)

70 x 10⁵

11.

How would you write 4.3756 x 10⁴in standard form?

a)

437,560,000

b)

0.00043756

c)

43,756

d)

4,3756

12.

Write log_b(xy) as two logs

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

13.

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

a)

log 98

b)

log 78

c)

log 56

d)

log 45

14.

a)

log (a⁵+ b²⁵)

b)

log (a⁵− b²⁵)

c)

log (ab²⁵)

d)

log (a⁵/b²⁵)

15.

a)

log₅(x²z²y¹⁰)

b)

log₅(z²y²x¹⁰)

c)

log(zy²x¹⁰)

d)

log₅(z² + y²+ x¹⁰)

16.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

17.

Convert to Exponential Form

$\log_ba=c$

a)

$c^b=a$

b)

$b^c=a$

c)

$b^a=c$

d)

$a^b=c$

e)

$a^b=c$

18.

Evaluate

$\log_464$

a)

3

b)

16

c)

$\frac{1}{3}$

d)

-16

e)

-3

19.

Convert to Logarithmic Form

$u^{-14}=v$

a)

$\log_u\left(-14\right)=v$

b)

$\log_uv=\frac{1}{14}$

c)

$\frac{1}{\log_uv}=14$

d)

$\log_uv=-14$

20.

Evaluate

$\log_41$

a)

0

b)

1

c)

4

d)

$\frac{1}{4}$

e)

Not Defined

21.

Which expression represents g(f(x)) if f(x) = 2x - 8
and
g(x) = 4x

a)

8x - 32

b)

8x² - 32x

c)

8x - 8

d)

6x - 8

22.

a)

9 - √17

b)

4

c)

2

d)

√8

23.

Find the inverse of $y=\ln\left(x+3\right)$

a)

$y=e^x-3$

b)

$y=e^{x-3}$

c)

$y=e^x+3$

d)

$y=e^{x+3}$

24.

Simplify: $e^{\ln40\ }$

a)

40

b)

-40

c)

e

d)

ln

25.

Find the inverse of y=9^x

a)

y=log_x9

b)

y=log₁₀9

c)

x=log_y9

d)

y=log₉x

26.

Which transformation best matches this set of data? The graphed function is f(x)

a)

g(x) = f(x) + 3

b)

g(x) = f(x - 2) - 3

c)

g(x) = f(x + 2) - 3

d)

g(x) = f(x + 2) + 3

27.

What are the transformations of the following polynomial from the parent function $f\left(x\right)=x^3$ ?

g\left(x\right)=-2\left(x+1\right)^3

a)

Vertical compression by a factor of 2, and shifted right by 1 unit

b)

Reflected over the x-axis, vertical stretch by a factor of 2, and shift left by 1 unit

c)

Reflected over the y-axis by a factor of 2, and shifted up by 1 unit

d)

Reflected over the x-axis, horizontal compression by a factor of 2, and shifted down by 1 unit

28.

Name the parent function.

a)

linear

b)

quadratic

c)

cube root

d)

cubic

29.

Write an absolute value function given the following transformations:
Reflection across the x-axis
Vertical shift right 2 units
Horizontal shift down 7 units

a)

y = -|x + 2| - 7

b)

y = |x - 2| - 7

c)

y = -|x - 2| - 7

d)

y = -|x - 2| + 7

30.

Which property of logarithms is demonstrated below:

\log_920\ =\ \frac{\log20}{\log9}

a)

Product property

b)

Quotient property

c)

Power property

d)

Change of Base Property

31.

Use the change of base property to rewrite as a single logarithm:

$\frac{\log15}{\log3}$

a)

$\log\ \frac{1}{5}$

b)

$\log5$

c)

$\log_{15}3$

d)

$\log_315$

32.

If $\log_BA=\frac{\log_nA}{\log_nB}$ , then $\log_{25}3=$

a)

$\frac{\ln25}{\ln3}$

b)

$\ln\frac{25}{3}$

c)

$\frac{\ln3}{\ln25}$

d)

$\ln\frac{3}{25}$

33.

Simplify $\sqrt[]{2+\sqrt[]{x}}=3.$

a)

5

b)

7

c)

49

d)

81

34.

Solve the equation $\sqrt[]{5+\sqrt[]{x-1}}=4.$

a)

8

b)

11

c)

121

d)

122

35.

Solve the equation $\sqrt[]{7+\sqrt[]{2x+3}}=5.$

a)

145.5

b)

157.5

c)

160.5

d)

162.5

36.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(3\right)\right)$

a)

34

b)

71

c)

35

d)

142

37.

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

38.

When f(x) = 2x and g(x) = x²+3 , find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

39.

a)

$16x+10$

b)

$-2x+6$

c)

$-16x-20$

d)

$-16x+6$

e)

$12x-14$

40.

Find the inverse of f(x) = x² - 5

a)

f^-1(x) = √(x) + 5

b)

f^-1(x) = ∛(x-5)

c)

f^-1(x) = ±√(x+5)

d)

f^-1(x) = x² - 5

Midterm Exam Reviewer

Total questions: 40

Worksheet time: 4hrs 32mins

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